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©2003 Algorithmics Inc.1
Risk Measurement
Risk Architecture
and the
Bank of the Future
Ron Dembo Founding Chairman
Algorithmics Incorporated
May, 2004Know Your Risk
©2003 Algorithmics Inc.2
Overview
1. Measuring Risk: The scale of the problem
2. State of the Market
3. Risk Architecture
4. Simulation, Static and Dynamic (Mark-to-Future)
5. Optimization
6. Potential topics for research
©2003 Algorithmics Inc.3
Open Research
1. Scenario Generation
2. Portfolio Compression
3. Pricing in Illiquid Markets
4. Near-Time Risk for a Large Institution
©2003 Algorithmics Inc.5
A Portfolio in the Future
Fre
qu
ency
Value
t n
Timet o
+
0
Distribution (tn) = F {price, yields ( many currencies), correlations,
growth rates, exchange rates, volatility surfaces, etc.}
©2003 Algorithmics Inc.6
Derivatives“Weapons of mass destruction”
“The only thing we understand is that we don’t understand how much risk the institution is running.”
Warren BuffetFortune, March 17, 2003
©2003 Algorithmics Inc.7
Know your Risk
….we have a liability of 350 million due April…..
….drop 2 notches is credit rating and this becomes
9 Billion!
“…..we have a liability of 350 million due April……”
or………
Enron
©2003 Algorithmics Inc.8
Know your Risk
JP Morgan (Enron)
Day 1: Exposure = $500 Million
Day 5: Exposure = $1 Billion
Day 12: Exposure = $1.9 Billion
What is the real exposure?
©2003 Algorithmics Inc.9
Know your Risk
NortelLargest company in Canada by Market Cap (= Mutual Funds)
30% drop in a day!
> 10 Billion Market Loss
Compensation Risk!
©2003 Algorithmics Inc.10
Know your Risk
HSBCOne of the largest banks in the world
> 60 trading floors
> 90 countries
> 4000 traders
> 300 “Enron” sized counterparties
Each with many subsidiaries, trading with any part of the bank
©2003 Algorithmics Inc.11
Branch
Division
Subsidiary
Corporate group
Counterparty
SIC
Country
All
TypeAll
Group
Maturity
Risk Taker
Risk On
ProductSet
What is my regulatory capital
on retail mortgages for UK division ?
What is my regulatory capital
on retail mortgages for UK division ?
What is my total Capital requirement
for the bank ?
What is my total Capital requirement
for the bank ?
What is my exposure, expected loss and regulatory capital
for United Airlines ?
What is my exposure, expected loss and regulatory capital
for United Airlines ?
What is my regulatory capital
against tech sectorfor our Asian sub ?
What is my regulatory capital
against tech sectorfor our Asian sub ?
What is my economic capital
for North Americansubsidiary ?
What is my economic capital
for North Americansubsidiary ?
What is my exposure and
regulatory capital tonon-investment grade products ?
What is my exposure and
regulatory capital tonon-investment grade products ?
What is my exposure And regulatory capital associated with Brazil ?
What is my exposure And regulatory capital associated with Brazil ?
“Simple” Questions
©2003 Algorithmics Inc.12
Coherent Measures & Credit RiskSingle Corporate 8% zero bond, 1 year maturity
Payoff (1 year): $108 99.89% (no default) $ 54 .. 0.11% (default)
VaR (99%) = $ 0.00
©2003 Algorithmics Inc.13
Coherent Measures & Credit RiskPortfolio of 10 independent bonds same characteristics
Payoff (1 year): $108 / 10 98.9% (no default)
$ 54 / 10 .. 1.1% (default)
VaR (99%) = $ 5.40 More diversified ====> More
Risk ???
©2003 Algorithmics Inc.15
At the end of the day….
Mark-to-Market
Mark-to-Future
Downside
Upside
+
+
+
-
-
©2003 Algorithmics Inc.16
Simulation (the Upside)
+
+
The Upside has the payoff of a Call option on net exposure !
+ +
The Horizon
Max{0, (Mx - eq´x)}
©2003 Algorithmics Inc.17
-
Simulation (the Downside)
-
-
The Downside is a Put option on net exposure !
-
Max{0, -(Mx - eq´x)}The Horizon
©2003 Algorithmics Inc.18
Decomposing a Risky Decision
Put
Call
Inherently forward-looking !
(Mx - eq´x)+
(Mx - eq´x)-
©2003 Algorithmics Inc.19
Risk-Adjusted Performance
++ -
Upside Downside -
Regret
(Call)
(Equity)
(Put)
(Debt)
©2003 Algorithmics Inc.20
The “Put / Call” Efficient Frontier
Put
Call
Maximize: Upside Subject to: Limited Downside
©2003 Algorithmics Inc.21
Risk-Adjusted Performance
Exposure
Call - Put
Concave function of net exposure
++ -
©2003 Algorithmics Inc.22
The “Put / Call” Efficient Frontier
Max: p´u
Subject to: p´d k ()
where: u - d - (Mx -rq´x) = 0 ( )
u 0; d 0
u´d = 0
©2003 Algorithmics Inc.23
Dual of “Put / Call” Trade-off
Min: kµ
Subject to: (M - rq´)´ = 0 (x)
p - µp 0 (u,d)
µ 0
Max: p´u
Subject to: p´d k ()
where: u - d - (M - rq´)x = 0 ()
u 0; d 0
©2003 Algorithmics Inc.24
Dual of “Put / Call” Trade-off
Min: kµ
Subject to: (M - rq´)´ = 0 (x)
p - µp 0 (u,d)
µ 0
Dual feasibility (r = 1) implies:
M´(/) = q
+
+
+
-
-
(/)
©2003 Algorithmics Inc.25
Complementarity
Min: kµ
Subject to: (M - rq´)´ = 0 (x)
p - µp 0 (u,d)
µ 0
Max: p´u
Subject to: p´d k ()
where: u - d - (M - rq´)x = 0 ( )
u 0; d 0
´{u - d - (M - rq´)x} = 0
©2003 Algorithmics Inc.26
Complementarity
´{u - d - (M - rq´)x} = 0
(/)´u - (/)´d = (/)´(Mx - q´x)
Call - Put = Future Gain/Loss
Complementarity iff Put / Call parity !
©2003 Algorithmics Inc.27
Modelling Liquidity
Price
Quantity
Price vs. Quantity is piecewise linear
(x1)L x1
(x1 )U
x = x1 + x2 + x3
0 x2 (x2)U
“fill” (x1)
before (x2)
before (x3)
0 x3 (x3)U
©2003 Algorithmics Inc.28
The Put/Call Efficient Frontier
Call(k)
k
k - (U) xU + (L) xL
(Put)
kinfinite liquidity )
Adjustment for liquidity
©2003 Algorithmics Inc.29
Prices in an Illiquid Market
Put
Call
Different tolerances for downside lead to different risk neutral discount factors
3
2
©2003 Algorithmics Inc.31
Single Period, Multi State
Security Prices
q1
q2 c
q3
m11
m21 1
m31
m12
m22 2
m32
m13
m23 3
m33
State Values 2
3
1
Probabilities
benchmarkportfolio
©2003 Algorithmics Inc.32
“Regret” Based Efficient Frontier
MR(K) = Minimize x ..... E ( ||(MTx - )||- )
Subject to : [E {MTx} -qTx] - [ E {} - c] > K
portfolio gain - target gain
Regret
©2003 Algorithmics Inc.33
A “Nobel” Quote
“…I should have computed the historical covariance of the asset
classes and drawn an efficient frontier….Instead I visualized my
grief if the stock market went way up and I wasn’t in it…or if it
went way down and I was completely in it. My intention was to
minimize my future regret, so I split my contributions 50/50
between bonds and equities..”
Harry Markowitz
(Money Magazine 1997)
©2003 Algorithmics Inc.34
Images of a Portfolio Inverse problems
Value
t
Time+
0
Portfolio
?
p1
p2
p3
Implied Views
Stability of Optimal solutions
No-arbitrage (risk-neutral) parameters (implied discount factors, distributions)
©2003 Algorithmics Inc.35
Immunization US Govt. Bond Portfolio
RangesGovt. Book
PV01 Hedge
Scenario Opt. Hedge
©2003 Algorithmics Inc.36
Immunization
99% Confidence VaR
US Govt Book $6,480,000
.. With PV01 Hedge $2,275,344
.. With Scenario-Optimal Hedge $353,634
©2003 Algorithmics Inc.37
Portfolio Compression
Portfolio: 1,025 Positions
Composition: Options on Bond Futures 4.9%
Callable Bonds 4.8%
Caps/Floors 32.3%
Bond Futures 1.6%
Interest Rate Swaps 15.5%
Treasury Bills, Bonds, Strips 40.9%
Replication with hypothetical Treasury Strips, European Options on long-dated Treasury Bonds, spanning monthly periods from January 1995 to December 2025
©2003 Algorithmics Inc.38
Compressed Portfolio
Compressed Portfolio: 51 Positions (simple)
Scenario Set: 50 randomly generated
Composition: 17 puts on long-dated Treasury Bonds
32 calls on long-dated Treasury Bonds
2 Treasury Strips
Replication with hypothetical Treasury Strips, European Options on long-dated Treasury Bonds, spanning monthly periods from January 1995 to December 2025
©2003 Algorithmics Inc.39
VaR Original (95%) 14,963,188
VaR Compressed (95%) 14,981,115
Error < 5 basis points!
TIME ( Compressed )TIME ( Original)
Compression Results
< 1 / 1000
©2003 Algorithmics Inc.41
Risk Computation Needs
Real-time IntradayOvernight
A single risk architecture must be able to handle business needs ranging from overnight batch to real-time
©2003 Algorithmics Inc.42
Risk Computation Needse.g. Counterparty credit exposures
Real-time IntradayOvernight
Baseline exposure profile
“Round robin” 24x7 updating Pre-deal checking
©2003 Algorithmics Inc.43
Risk Architecture
Monolithic vs Distributed
Intraday possibleInherently slow
©2003 Algorithmics Inc.44
Distributed Architecture
Data
Risk Engines
Output
Multiple data sources
communicating with multiple risk engines
producing output in multiple locations
all interconnected !
©2003 Algorithmics Inc.46
Scenario based
Links all risk types
Full forward valuation, no shortcuts
Separates simulation and reporting
Mark-to Future
©2003 Algorithmics Inc.47
An example of the complexities
The floating leg of a swap:
now
value date
Bond
Bond
age
age
©2003 Algorithmics Inc.48
An example of the complexities
The floating leg of a swap:
now
value date
reset date…
reset rate
present value
indexing
Monte-C
arlo generation
©2003 Algorithmics Inc.50
MtF of a Portfolio
Scenarios
Any
Portfolio MtF
sort
statistics
3 16 45 5
All Instruments
(MtF)
©2003 Algorithmics Inc.51
Mark-to-Future Values
MtFCube MappingS
cena
rios
Sce
nario
s
Mark-to-Future
Instruments
Mark-to-Future
Credit Portfolio
Netting,Netting,Credit MitigationCredit MitigationCollateral, etc.Collateral, etc.
©2003 Algorithmics Inc.52
Mapping to Basis Instruments
Risk Factor
3 month rate6 month rate1 year rate 5 year rate
Product
Bond
Basic Instrument
3M Zero 6M Zero 1Y Zero5Y Zero
e.g.
©2003 Algorithmics Inc.53
Maps for Equities
MtM
MtF
=m21
m31
m11
m21
m31
m11
m21
m31
m11
213
++ d2
d3
d1
Scenarios
Factor MtF (done once!)
f11 + f2 2 + f33
Stock or portfolio of stocks
Is mapped into
a portfolio of factors
©2003 Algorithmics Inc.54
A Swap Portfolio
Single Currency; 40,000 (Vanilla) Swaps20 points on yield curve; 1000 scenarios; 10 time periods
1020
1000 = 200,000!
Swap Portfolio = F(m1,…,m20 )
Risk in an instant!
©2003 Algorithmics Inc.55
“Real Time” Mark to Future
MtF Incremental Deal Full MtF Exposure Calc Statistics
Simulation Aggregation
Heavy Light
Counterparty portfolio:• 2000 positions
• FRAs, FX Forwards & Options, IRS, Caps/Floors, Swaptions etc… (long & short positions)
• 83 risk factors
• 1000 scenarios across 50 time steps
• netting agreements & collateral
Pre-deal ‘what-if’ for new interest rate swap with a counterparty:
Total simulation and aggregation time to derive a full montecarlo updated profile: 13 seconds!!!!
©2003 Algorithmics Inc.56
Consistency
Consistent Measurement of Earnings and Value at Risk
Scenarios
Growth and
re-investment
assumptions
Cash flow
generation
Valuation
Models
Earnings-at-Risk
Value-at-Risk
Pre-cube Post-cube
©2003 Algorithmics Inc.57
Without the “cube”, scalability to 20,000 users in real time would be prohibitive!
Mark-to Future
©2003 Algorithmics Inc.58
Only a few scenarios are relevant!
Mean of Distribution (10,000 scenarios)
11 “Bucket Scenarios” reproduce the distribution for 1/1000th the work!
Mean of a Bucket
Single scenario result
©2003 Algorithmics Inc.60
Dynamic Portfolios
Time
Events
Portfolio changes
Function of the scenarios and strategy
©2003 Algorithmics Inc.61
A Regime
If( margin on the derivatives book is below s, liquidate sufficient bonds to raise it to S)
Apply to all marked nodes
A “Regime”
©2003 Algorithmics Inc.62
Funding Liquidity Risk
Cash /Collateral Account
Time
Multiperiod Simulation
©2003 Algorithmics Inc.64
ConvergenceRegulatory Capital and Economic Capital will converge
Asset Liability
Management
Market Risk
Management
1970 - 1979 1980 - 1989 1990 - 1999 2000+
Gap AnalysisDuration
Sensitivity
Parallel Shifts
Stress Tests
Earnings Simulation
Parametric VaR
Fair Accounting Value
Scenario Based VaR
Integrated
ERM
Basel 1 Basel 2
©2003 Algorithmics Inc.65
State of the Enterprise Risk Market(Banks) Mapped to Products
Innovators
EarlyAdopters
EarlyMajority
LateMajority
Laggards(Skeptics
)
Operational Risk
Collateral
Credit risk
Market risk
Market
Matu
rity
Risk Architecture
©2003 Algorithmics Inc.66
State of the Enterprise Risk Market(Asset Managers) Mapped to Products
Innovators
EarlyAdopters
EarlyMajority
LateMajority
Laggards(Skeptics
)
Operational Risk
Collateral
Credit risk
Market risk
Market
Matu
rity
Risk Architecture
©2003 Algorithmics Inc.67
State of the Enterprise Risk MarketMapped to Regulations
Innovators
EarlyAdopters
EarlyMajority
LateMajority
Laggards(Skeptics
)
Basel II
Basel I
Market
Matu
rity
Patriot ActFSA 195Sarbanes-Oxley
FAS 133
©2003 Algorithmics Inc.68
The Regulatory Environment
Basel II is a regulatory framework for risk measurement
• Market Risk (as in previous accord)• Credit Risk (a fundamental change)• Operational Risk (new)
Just think back to the fundamental changes to risk management
practice brought about by Basel I.
Basel II will result in much bigger changes.
©2003 Algorithmics Inc.69
“institutions wishing to qualify . . . will have to prove . . .that the internal ratings system and its component parts are all used in the active day-to-day granting of credit.”
From the New Basel Accord.
• pricing of credit risk
• incorporation of credit mitigation
• setting of credit limits
• calculation of economic capital
Use test to qualify for waiver
©2003 Algorithmics Inc.70
Basel II Highlights
The biggest change will occur in the measurement and management of credit:
• credit touches all aspects of banking
• significant amount of new sophistication in credit measurement infrastructure
• usage criteria will require banks to re-engineer their IT architecture
©2003 Algorithmics Inc.71
Basel II ..some quotes
“…..Basel II is nice, but we are re-architecting our credit infrastructure because it is good for business!”
…Tim Howell, Head Group Treasury, HSBC
In the first day of operation of its new credit risk system, HSBC saved more than the cost of the software!
©2003 Algorithmics Inc.73
A Fundamental Change
Today:
Banks do business and then compute risk
Tomorrow:
They will compute risk and then do business!
©2003 Algorithmics Inc.74
Traded Products (Non-Traded) Products
Capital Mkts
Market Risk
ERM
Capital Mkts
Credit Risk
ERM
Credit Risk
Limits
Asset
Liability
Credit
Risk
Banks Today
Limits Mgt.
Front
Middle
Limits Mgt.
Front
Middle
Back
Limits Mgt.
Front
Middle
Back
Limits Mgt.
Front
Middle
Back
Retail
Mortgages
Comm.
Lending
Credit
Cards
Back
Swaps FxCreditDerivatives
Emerging
Markets
Collateral
©2003 Algorithmics Inc.75
ConvergenceRegulatory Capital and Economic Capital will converge
Asset Liability
Management
Market Risk
Management
1970 - 1979 1980 - 1989 1990 - 1999 2000+
Gap AnalysisDuration
Sensitivity
Parallel Shifts
Stress Tests
Earnings Simulation
Parametric VaR
Fair Accounting Value
Scenario Based VaR
Integrated
ERM
Basel 1 Basel 2
©2003 Algorithmics Inc.76
Enterprise Risk Today
Banks today are a collection of Independent silos
Bank of today
Enterprise risk is an adjunct to the operation (one way)
Eq
uit
y
Sw
aps
FX
Bon
ds
©2003 Algorithmics Inc.78
The Bank of the Future
Eq
uit
y
Sw
aps
FX
Bon
ds
Risk computation will no longer be an adjunct to the business, it will be at the core
©2003 Algorithmics Inc.79
Vision….usage scenarios
A global investment bank 8 am any day of the week
You are the CFO for the Global Credit Operation and you have just come into your
office to review the P/L statement for your global loan portfolio. You download a
report that has undertaken a full mark-to-market for your loan book on a daily
basis.
Using credit spread curves that are updated daily using the bond and credit default
swap markets along with credit migrations from the day before you are able to
analyze your loan balance sheet on the same basis as your trading book --
including assessing the embedded optionality such as prepayment and credit line
utilization.
©2003 Algorithmics Inc.80
Conclusions
Today……….. enterprise risk systems are an adjunct to a bank
Tomorrow…... they will be central
Up until today.. risk architecture has not been so important
Tomorrow…… it will separate high performing banks from under-performers